Mathematics questions
18011 published questions with worked solutions.
- If the set of all solutions of |x² + x − 9| = |x| + |x² − 9| is [α, β] ∪ [γ, ∞), then (α² + β² + γ²) is equal to:
- Let z be a complex number such that |z + 2| = |z − 2| and arg ( z+3 z-i ) = 4. Then |z|² is equal to:
- The number of functions f : 1, 2, 3, 4 → a, b, c , which are not onto, is:
- Let S = A = bmatrix a & b c & d bmatrix : a,b,c,d 0,1,2,3,4 and A^2 - 4A + 3I = 0 be a set of 2 × 2 matrices. Then the number of...
- Let A = bmatrix 1 & 1 & 2 -2 & 0 & 1 1 & 3 & 5 bmatrix . Then the sum of all elements of the matrix adj(adj(2(adjA)⁻¹)) is equal...
- The first term of an A.P. of 30 non-negative terms is 10 3. If the sum of this A.P. is the cube of its last term, then its common...
- The number of ways of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:
- Let the smallest value of k ∈ ℕ, for which the coefficient of x³ in (1+x)³ + (1+x)⁴ + (1+x)⁵ + … + (1+x)⁹⁹ + (1+kx)¹⁰⁰, x ≠ 0, is...
- Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b, 13, 67, (a > b), are 40 and 21,...
- Let the vertex A of a triangle ABC be (1, 2), and the mid-point of the side AB be (5, −1). If the centroid of this triangle is...
- Suppose that two chords, drawn from the point (1, 2) on the circle x² + y² + x − 3y = 0 are bisected by the y-axis. If the other...
- A line with direction ratios 1, −1, 2 intersects the lines x2 = y3 = z+1 3 and x+1 -1 = y-2 1 = z4 at the points P and Q,...
- The square of the distance of the point (−2, −8, 6) from the line x-1 1 = y-1 2 = z -1 along the line x+5 1 = y+5 -1 = z2 is...
- If y = ^ -1 ( 3 x - 4 x 4 x + 3 x ) + 2 ^ -1 ( x 1+ 1-x^2 ), then dy dx at x = 3 2 is equal to:
- The area of the region (x,y) : y ≤ π − |x|, y ≤ |x sinx|, y ≥ 0 is:
- Let _ -2 ^ 2 (| x| + [x x])dx = 2(3- 2) + , where [·] is the greatest integer function. Then ( 2 ) equals:
- Let y = y(x) be the solution of the differential equation dy dx = (1+x+x^2)(1-y+y^2), y(0) = 12. Then (2y(1) − 1) is equal to:
- A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in...
- Consider the parabola P : y² = 4kx and the ellipse E : x^2 a^2 + y^2 b^2 =1. Let the line segment joining the points of...
- If A = 3° 9° + 9° 27° + 27° 81° and B = 81° - 3°, then BA is equal to _______.